You can fly into Ercan airport (Lefkosa) in North Cyprus but you can only do this by going via Turkey.

Or you can go to Larnaca airport in the south.

If you would like to hire a car in the south and drive it north, I have the details of a hire car company whose cars are registered to do that. You have to buy insurance at the TRNC border (20 euros) for the car. You can go through Pyla border.

Or I know a hire car company in the north who will send a taxi for you from the airport and then take you to the car. You cannot take these cars south as they are not registered.

I am happy to advise either way.